Date of Award
August 2018
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Hans Volkmer
Committee Members
Hans Volkmer, Peter Hinow, Gabriella Pinter, Jeb Willenbring, Dexuan Xie
Keywords
flat-ring coordinates, internal and external harmonics
Abstract
The goal of this dissertation is to derive expansions for a fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. These expansions are in terms of harmonic functions in the interior and the exterior of two different types of regions, "flat rings" and "peanuts" according to their shapes. We solve Laplace's equation in the interior and the exterior of these regions using the method of separation of variables. The internal and external "flat-ring" and "peanut" harmonic functions are expressed in terms of Lamé functions.
Recommended Citation
Bi, Lijuan, "Internal and External Harmonic Functions in Flat-Ring Coordinates" (2018). Theses and Dissertations. 1751.
https://dc.uwm.edu/etd/1751